%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-7-11 on page II-201 in "Ghostbusters\texttrademark ".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{147.0pt}
%StartShownPreambleCommands
\usepackage{amsmath}
%StopShownPreambleCommands

\begin{document}
\[  f_p (x) =
 \begin{cases}
   \frac{1}{\smash[b]{p}}  & x = p  \\   % smash added
   \frac{{}                                     % and
         \smash[t]{\frac{(1 - x)^{\frac{1}{2}}} % here
                        {  x - \sin (x - p)   } } }
        {\sqrt{1 - p} \, \cos (x - p)}  & x \neq p
 \end{cases}  \]
\end{document}
